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5 Answers
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The online chinese dictionary MDBG provides radical information for every character in its database. For instance, if you search for the character 天 (tiān) and click on the first result, the "Rad/Str" column reads 大 + 1, i.e., the radical 大 plus one stroke.

Zhongwen.com also gives information on character decomposition. The entry for 洋 reads "Water 水 with 羊 phonetic."

As Alenanno pointed out, not all parts of characters are radicals, but these two resources can give you more information about how characters are constructed.

You seem to assume that characters are only done by radicals, which is not true. Not all parts in a character are radicals.

Consider for example the character 他. The radical is 亻 which is 人, the other part is not a radical; its appearance is the same as the character for "also": 也, but this is not a radical. Radicals are very useful, since you can understand the probable "topic-area" of a character:

烊 has the radical 火 (fire), and means "melt"; 洋 has the radical 水 (water), and means ocean.

In the case of 天, the radical is the #37 in this page, which is 大 + another stroke (4 strokes in total).

If you want to learn characters by stroke, (for example for the character 天) you can use some sites that help you with animations/pictures showing the stroke order; you can also start from the wikipedia resources regarding stroke orders.

天 in ancient Chinese means the head of a person. And hence, it is designed to use a stroke (一) to indicate the position of the head of a person (大=人). Later, its meaning changed to the sky that is something above (一) a person(大). Not all kanji are designed by radicals. This design of 天 is called 指示字, which literally means a word designed by indication. For example, 刑天, which literally means Cut-off(刑) Head(天), is a rebel general in ancient Chinese legend with his head cutting of by 皇帝 (emperor of ancient China).
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jichiMay 6 at 15:28